Title
Statistička teorija uzročnosti, stohastičke diferencijalne jednačine i svojstvo martingalne reprzentacije
Creator
Valjarević, Dragana, 1976-
Copyright date
2013
Object Links
Select license
Autorstvo 3.0 Srbija (CC BY 3.0)
License description
Dozvoljavate umnožavanje, distribuciju i javno saopštavanje dela, i prerade, ako se navede ime autora na način odredjen od strane autora ili davaoca licence, čak i u komercijalne svrhe. Ovo je najslobodnija od svih licenci. Osnovni opis Licence: http://creativecommons.org/licenses/by/3.0/rs/deed.sr_LATN Sadržaj ugovora u celini: http://creativecommons.org/licenses/by/3.0/rs/legalcode.sr-Latn
Language
Serbian
Cobiss-ID
Inventory ID
D-2639
Theses Type
Doktorska disertacija
Other responsibilities
mentor
Petrović, Ljiljana, 1956-
član komisije
Janković, Svetlana, 1949-
član komisije
Bojović, Dejan, 1968-
Academic Expertise
Prirodno-matematičke nauke
University
Univerzitet u Kragujevcu
Faculty
Prirodno-matematički fakultet
Group
Katedra Instituta za matematiku i informatiku
Publisher
Kragujevac : [D. Valjarević],
Format
PDF/A (listova)
description
datum odbrane: 22.06.2013.
Abstract (en)
One of the important and basic goals of science is to establish cause-e®ect re-
lations between events. Many discussions were about the concept of causality and
how it can be measured. The concept of Granger's causality (Granger, 1969) is very
well known in economy and it can be applied in researches. Granger's de¯nition of
causality is based on the idea that the present and the future cannot e®ect the past. About the concept of causality have been discussed for a very long time in all areas of science. In last decade we are dealing with a signi¯cant progress.
Today, a concept of causality have a wide application in physical, biological andsocial sciences, history, medicine, especially in epidemiology, economy and etc.
The area of research of this Phd dissertation is statistical theory of causality and its application on weak solutions of stochastic di®erential equations and martingale representation property. It have been shown that this concept of causality is equivalent with the concept of weak uniqueness of weak solutions for the stochastic di®erential equations and extremal solutions of the martingale problem. This concept of causality can be characterized with stopping times and its connection with extremal solution of the stopped martingale problem can be proved, as well as with locally unique weak local solutions.
The concept of causality can be related to the theory of martingales, too. Namely, this concept can be connected with the preservation of the martingale property, orthogonal martingales, stable subspaces as well as with martingale representation property, which have an application, especially in ¯nancial mathematics.
Classification
517.91(043.3)
Subject
Diferencijalne jednačine
Type
monograph
manuscript text - theses
Text
Abstract (en)
One of the important and basic goals of science is to establish cause-e®ect re-
lations between events. Many discussions were about the concept of causality and
how it can be measured. The concept of Granger's causality (Granger, 1969) is very
well known in economy and it can be applied in researches. Granger's de¯nition of
causality is based on the idea that the present and the future cannot e®ect the past. About the concept of causality have been discussed for a very long time in all areas of science. In last decade we are dealing with a signi¯cant progress.
Today, a concept of causality have a wide application in physical, biological andsocial sciences, history, medicine, especially in epidemiology, economy and etc.
The area of research of this Phd dissertation is statistical theory of causality and its application on weak solutions of stochastic di®erential equations and martingale representation property. It have been shown that this concept of causality is equivalent with the concept of weak uniqueness of weak solutions for the stochastic di®erential equations and extremal solutions of the martingale problem. This concept of causality can be characterized with stopping times and its connection with extremal solution of the stopped martingale problem can be proved, as well as with locally unique weak local solutions.
The concept of causality can be related to the theory of martingales, too. Namely, this concept can be connected with the preservation of the martingale property, orthogonal martingales, stable subspaces as well as with martingale representation property, which have an application, especially in ¯nancial mathematics.
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